nLab magic pyramid

Idea

The classification of pure supergravity theories in dimensions 3,4,6,10 and 4,5,7,11 is parameterized by the real normed division algebras, while the classification of super Yang-Mills theories is parameterized by pairs of real normed division algebras, see at supersymmetry and division algebra and at spin representation.

Combining this yields a classification of the extended super Einstein-Yang-Mills theories by triples of real normed division algebras. called a magic pyramid of supergravity theories (ABDHN 13).

(from ABDHN 13, p. 3)

In this diagram vertical axis labels the spacetime division algebra (hence vertical label $\mathbb{R}$ corresponds to $d = 2+1$, vertical label $\mathbb{C}$ to $d = 3+1$, $\mathbb{H}$ to $d = 5+1$ and $\mathbb{O}$ to $d = 9+1$) , while the horizontal axes label the algebras associated with the number of left and right supersymmetries. The entries display the corresponding U-duality groups. Each horizontal level is a “magic square”.

Related concepts

• magic supergravity

• KLT relations

References

• A. Anastasiou, Leron Borsten, Mike Duff, L. J. Hughes, S. Nagy, A magic pyramid of supergravities, Journal of High Energy Physics, April 2014, 2014:178, (arXiv:1312.6523)

based on

• Leron Borsten, Mike Duff, L. J. Hughes, S. Nagy, A magic square from Yang-Mills squared, Phys. Rev. Lett. 112, 131601 (2014) arXiv:1301.4176

• A. Anastasiou, Leron Borsten, Mike Duff, L. J. Hughes, S. Nagy, Super Yang-Mills, division algebras and triality (arXiv:1309.0546)